A new generalization of t-lifting modules

Document Type : Research Paper

Authors

1 University of Mazandaran, Babolsar, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran

3 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

4 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar

Abstract

In this paper we introduce the concept of $tCC$-modu\-les which is a proper generalization
of ($t$-)lifting modules. Let $M$ be a module over a ring $R$.
We call $M$ a $tCC$-module
(related to $t$-coclosed submodules) provided that for every
$t$-coclosed submodule $N$ of $M$, there exists a direct summand $K$ of $M$
such that $M=N+K$ and $N\cap K\ll K$.
We prove that a module with $(D_3)$ property is $tCC$
if and only if every direct summand of $M$ is $tCC$. It is also shown
that an amply supplemented module $M$ is $tCC$ if and only if $M$ decomposed to
$\overline{Z}^2(M)$ and a submodule $L$ of $M$ that both of them are $tCC$.

Keywords

Journal of Algebra and Related Topics
Volume 8, Issue 1
June 2020
Pages 1-13

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